In the wake of the ongoing deregulations of the electric power markets, load transmission and wheeling of power from distant generators to local consumers has become common practice. As a consequence of the competition between utilities and the emerging need to optimize assets, increased amounts of electric power are transmitted through the existing networks, invariably causing congestion, transmission bottlenecks and/or oscillations of parts of the power transmission systems. In this regard, electrical transmission networks are highly dynamic. In general, electromagnetic oscillations in electric power systems comprising several alternating current generators have a frequency of less than a few Hz and are considered to be acceptable as long as they decay. They are initiated by the normal small changes in the system load, and they are a characteristic of any power system.
However, insufficiently damped oscillations may occur when the operating point of the power system is changed, for example, due to a new distribution of power flows following a connection or disconnection of generators, loads and/or transmission lines. Likewise, the interconnection of several existing power grids, even if one or more of the existing grids do not individually present any poorly damped oscillations prior to their interconnection, may give rise to insufficiently damped oscillations. In these cases, an increase in the transmitted power of a few MW may make the difference between stable oscillations and unstable oscillations which have the potential to cause a system collapse or result in lost of synchronism, lost of interconnections and ultimately the inability to supply electric power to the customer. Appropriate monitoring of the power system can help a network operator to accurately assess power system states and avoid a total blackout by taking appropriate actions such as the connection of specially designed oscillation damping equipment.
Electric power transmission and distribution systems or networks comprise high-voltage tie lines for connecting geographically separated regions, medium-voltage lines, and substations for transforming voltages and for switching connections between lines. For managing the network, it is known to utilize Phasor Measurement Units (PMU). PMUs provide time-stamped local information about the network, such as currents, voltages and load flows. A plurality of phasor measurements collected throughout the network by PMUs and processed at a central data processor can provide a snapshot of the overall electrical state of the power system.
Patent Application EP-A 1 737 098 describes the combined voltage or power flow control and damping of single mode electromagnetic oscillations in an electric power system by Flexible AC Transmission System (FACTS) devices. To this end, information about a state or operating point of the power system is generated from suitable second system signals, and a control parameter of a FACTS controller is derived therefrom. The control parameter and first system signals are used in the calculation of a control command defining the settings of the FACTS device. Following a change in the state of the power system, such as a change in the topology of a transmission network, poorly damped or even unstable oscillations are avoided by appropriate re-tuning of the control parameter of the damping or stabilizing equipment.
Exemplary FACTS devices comprise power semiconductor components and include, by way of example, Static-Var Compensators (SVCs), Unified Power Flow Controller (UPFC), Thyristor-Controlled Series Capacitors (TSCSs), thyristor controlled phase-shifting transformers (TCPST), impedance modulators, and series compensation capacitors.
Such known technologies enable damping control of a selected single mode oscillation based on a single feedback signal. This is known as a single-input single-output solution (SISO). It has been found that electromechanical oscillations in electric power networks also take the form of a superposition of multiple oscillatory modes. These multiple oscillatory modes create similar problems to the single mode oscillations and thus have the potential to cause a collapse of the electric power network. Furthermore, in situations where a Power Oscillation Damping (POD) controller is used to stabilize a single selected oscillatory mode, this may often have the effect of destabilizing the other oscillatory modes present, for example, a second dominant mode, which is subsequently damped less than the first dominant mode. Thus, it can be seen that the second dominant mode (and any other mode) is negatively impacted by the performance of the SISO POD controller which is tuned to improve the damping of the first dominant oscillatory mode.
With reference to the known technologies which enable damping control of single mode oscillations, FIG. 1 shows a complex frequency domain graph of the effect of a known SISO POD controller utilizing local feedbacks. In such a complex frequency domain graph (in the s-plane), the x-axis represents the real part of s (which is absolute modal damping) and the y-axis represents the imaginary part of s (which is modal frequency in radians per second) where the s-plane transforms are commonly known as Laplace transforms; hence in the s-plane, multiplying by s has the effect of differentiating in the corresponding real time domain and dividing by s has the effect of integrating. Each point on the s-plane represents an eigenvalue or a transfer function pole. The arrow 10 closest to the x-axis represents the improvement of damping of the first dominant oscillatory mode, because the change of the eigenvalue is directed towards the left half of the complex plane. The parallel arrow 12 further from the x-axis represents the deterioration in damping of the second dominant oscillatory mode (increasing oscillations in the time domain) which is indicated by the change of the eigenvalue towards the right half of the complex plane.
The article “Application of FACTS Devices for Damping of Power System Oscillations”, by R. Sadikovic et al., proceedings of the Power Tech conference 2005, Jun. 27-30, St. Petersburg RU, is incorporated herein by reference. This article addresses the selection of the proper feedback signals and the subsequent adaptive tuning of the parameters of a power oscillation damping (POD) controller in case of changing operating conditions. The selection is based on a linearized system model, the transfer function G(s) of which is being expanded into a sum of N residues:
      G    ⁡          (      s      )        =            ∑              i        =        1            N        ⁢                  R        i                    (                  s          -                      λ            i                          )            
The N eigenvalues λi correspond to the N oscillation modes of the system, whereas the residue Ri for a particular mode gives the sensitivity of that mode's eigenvalue to feedback between the output and the input of the system.